Set up as if doing a standard long division
{:
(,,"-----","-----","-----"),
(n+2,")",n^2,-11n,-26)
:}
The leading term of the divisor color(green)(n) divides into the leading term of the dividend color(blue)(n^2), color(red)(n) times
{:
(,,color(red)(n),,),
(,,"-----","-----","-----"),
(color(green)(n)+2,")",color(blue)(n^2),-11n,-26)
:}
Multiply the divisor color(green)(n+2) by the term just written in the quotient (color(red)(n)) giving a product of color(cyan)(n^2+2n)
and subtract this product from the dividend giving a difference of color(blue)(-13n) and "bring down the next term, color(orange)(-26)
{:
(,,color(red)(n),,),
(,,"-----","-----","-----"),
(color(green)(n+2),")",n^2,-11n,-26),
(,,color(cyan)(n^2),color(cyan)(+2n),),
(,,"-----","-----",),
(,,,color(blue)(-13n),color(orange)(-26))
:}
Repeat this process to get:
{:
(,,n,-13,),
(,,"-----","-----","-----"),
(n+2,")",n^2,-11n,-26),
(,,n^2,+2n,),
(,,"-----","-----",),
(,,,-13n,-26),
(,,,-13n,-26),
(,,,"-----","-----"),
(,,,,0)
:}
